A cow is tied to a corner (vertex) of a regular hexagonal fenced area of side a metres by a rope of length 5a/2 metres in a grass field. (The cow cannot graze inside the fenced area.) What is the maximum possible area of the grass field to which the cow has access to graze ?

Options

A. `5 pi a^(2)`
B. `(5)/(2)pia^(2)`
C. `6 pi a^(2)`
D. `3pia^(2)`

Answer

A

Explanation

`"Area"=2[(120)/(360)xxpi((5a)/(2))^(2)+(60)/(360)xxpi((3a)/(2))^(2)+(60)/(360)xxpi((a)/(2))^(2)]`
`=(2 pi)/(3) [(25a^(2))/(4)+(9a^(2))/(8)+(a^(2))/(8)]`
`=(2pi)/(3)xx(30a^(2))/(4)=5 pi a^(2)`